I think it's a question of balance, depending on how strong a position you are.
If you are in a position of weakness, feeling sorry for yourself, recovering from something you are judging yourself on - then you absolutely should start with self-compassion, being kind to yourself.
To continue in this mode would ultimately hit your ambition and drive, so if you are in a bit of a stronger position mentally, a higher gear, then boosting your self-esteem is more important.
If you are in a position of weakness, feeling sorry for yourself, recovering from something you are judging yourself on - then you absolutely should start with self-compassion, being kind to yourself.
To continue in this mode would ultimately hit your ambition and drive, so if you are in a bit of a stronger position mentally, a higher gear, then boosting your self-esteem is more important.